The number of all integers n for which n² + 96 is a perfect square, is

What is the area of an equilateral triangle whose inscribed circle has radius R?

Given below are two statements: Statement I: The number of ways to pack six copies of the same book into four identical boxes, where a box can contain as many as six books, is 9. Statement II: The minimum number of students needed in a class to guarantee that there are at least s…

Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed and both P and Q can fill the remaining part in 7 hours. The number of hours that will be taken by R alone to fill the tank is

Given below are two statements: Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5. Statement II: A milkman adds 30 litres of water to 70 litres of milk…

A train running at 18 km per hour crosses a mark on the platform in 9 seconds and takes 25 seconds to cross the platform. If P is the length of the train and Q is the length of the platform in meters, then (P, Q) = ___________.

If x − 1/x = y, y − 1/y = z, z − 1/z = x, then which of the following equations are true? A. 1/x + 1/y + 1/z = 0 B. 1/x² + 1/y² + 1/z² = 8 C. 1/(xy) + 1/(yz) + 1/(zx) = −3 Choose the correct answer from the options given below:

What is the probability of getting a sum of 22 or more when four dice are thrown?

If 5ᵃ = 9ᵇ = 2025, then the value of ab/(a + b) = _____.